The concept of a "controlled aerodrome in non-controlled airspace" is, as far as I know, a UK-only phenomenon. In decent FIR's, airspace G (as mentioned in the opening post) means radio contact can never be mandatory, perhaps not even carrying the equipment thereto. But the opening post does not state in what FIR the flight operates.
That said, it never hurts to announce one's activities and intentions on the appropriate frequency.